a)
[tex]6:3-4\frac{3}{10}\cdot5=2-\frac{43}{10}\cdot5=\\\\=2-\frac{43}{2}=2-21,5=-(21,5-2)=\boxed{-19,5}[/tex]
b)
[tex]6\frac{2}{3}+1,21:\frac{11}{20}-4\frac{5}{12}=\\\\=6\frac{2}{3}+\frac{121}{100}\cdot\frac{20}{11}-4\frac{5}{12}=6\frac{2}{3}+\frac{11}{5}-4\frac{5}{12}=\\\\=6\frac{2}{3}+2\frac{1}{5}-4\frac{5}{12}=6\frac{40}{60}+2\frac{12}{60}-4\frac{25}{60}=\\\\=8\frac{52}{60}-4\frac{25}{60}=4\frac{27}{60}=4\frac{9}{20}=4\frac{45}{100}=\boxed{4,45}[/tex]
c)
[tex]5\frac{2}{5}\cdot(5\frac{1}{3}-4,5)^2=\frac{27}{5}\cdot(5\frac{1}{3}-4\frac{1}{2})^2=\\\\=\frac{27}{5}\cdot(5\frac{2}{6}-4\frac{3}{6})^2=\frac{27}{5}\cdot(\frac{5}{6})^2=\\\\=\frac{27}{5}\cdot\frac{25}{36}=3\cdot\frac{5}{4}=3\cdot1\frac{1}{4}=3\cdot1\frac{25}{100}=3\cdot1,25=\boxed{3,75}[/tex]